Question

Find each sum

$4+4.5+5+5.5+...+100$

Short answer

The solution is$S_{193}=10036$

Step-by-step solution

Given information

$4+4.5+5+5.5+...+100$

Calculation

We have,$4+4.5+5+5.5+...+100$

So, $a_1=4,d=0.5,a_n=100$

Now use formula,

$$\begin{gathered} a_n=a_1+(n-1)d \\ \Rightarrow 100=4+(n-1)0.5 \\ \Rightarrow 100=4+0.5n-0.5 \\ \Rightarrow 0.5n=96.5 \\ \Rightarrow n=193 \end{gathered}$$

To find sum $S_{193}$

$$\begin{gathered} S_{193}=\frac{193}{2}[4+100] \\ =10036 \end{gathered}$$